4S0 



SCIENCE OF AGRICl/LTURE. 



Part II. 



locks or liollows (6), or by smootli-headed stakes driven into the surface, and protruding 

 above, or sunk under it, according to the obstructions. 



3065. Lines of uniform declivity or acclivity (Jig. 420 e, e, e) are feadily formed on 

 the same principle. In this and the former case, the common level and the horning 

 pieces (a and d), with measuring-rods and stakes, arc all the instruments required. 



SuBSECT. 3. Of the Division and laying out of Lands. 



3066. The division of lands is one of the most important and not the least difficult 

 parts of the land surveyor's art. In intricate cases, as in the subdivision of large es- 

 tates or commons, the professional surveyor will generally be resorted to, but it is essen- 

 tial for the land-steward and proprietor, and even for the farmer, or professional Culti- 

 vator, to know the general principles on which this business is founded. We shall there- 

 fore shortly develope these principles from Dr. Hutton's valuable Dictionary, and next 

 offer some general rules of our own, for ordinary cases of dividing and laying out 

 lines. 



3067. In the division of commons, after the whole is surveyed and cast up, and the 

 proper quantities to be allowed for roads, &c. deducted, divide the net quantity remain- 

 ing among the several proprietors, by the rule of fellowship, in proportion to tlie real 

 value of their estates, and you will thereby obtain their proportional quantities of the 

 land. But as this division supposes the land, which is to be divided, to be all of an 

 equal goodness, you must observe that if the part in which any one's share is to be 

 marked off, be better or worse than the general mean quality of the land, then you 

 must diminish or augment the quantity of his share in the same proportion. 



3068. Or divide the ground among the claimants in the direct ratio of the value of their 

 claims, and the inverse ratio of the quality of the ground allotted to each ; that is, in 

 proportion to the quotients arising from the division of the value of each person's estate, 

 by the number which expresses the quality of the ground in his share. 



3069. But these regidar methods cannot always be put in practice ; so that, in the di- 

 vision of commons, the usual way is, to measure separately all the land that is of dif- 

 ferent values, and add into two sums the contents and the values ; then the value of 

 every claimant's share is found by dividing the wliole value among them in proportion 

 to their estates ; and lastly, a quantity is laid out for each person, that shall be of the 

 value of his share before found. 



3070. It is required to divide any given quantity of ground, or its valve, into any given 

 number of parts, and in proportion to any given number. Rule. Divide the given 

 piece, or its value, as in the rule of fellowship, by dividing the whole content or value 

 by the sum of the numbers expressing the proportions of the several shares, and mul- 

 tiplying the quotient severally by the said proportional numbers for the respective shares 

 required, when the land is all of the same quality. But if the shares be of different 

 qualities, then divide the numbers expressing the proportions or values of the shares, by 

 the numbers which express the qualities of the land in each share ; and use the quotients 

 instead of the former proportional numbers. 



Ex. 1. If the total value of a common be 2.%0/. it is required 

 to determine the values of the shares of the three claimants A, B, C, 

 whose estates are of these values, 10,000, and 15,000, and 25,000/. 

 The estates being in proportion as the numbers 2, 3, 5, whose sum is 10, 

 we shall have 2,5000 -?- 10= 250; which being severally multiplied by 2, 

 3, 5, the products 500, 750, 1250, are the values of the shares required. 



Ex. 2. It is required to divide 300 acres of land among A, B, C, D, E, 

 F, G, and H, whose claims upon it are respectively in proportion as the 

 numbers 1, 2, 3, 5, 8, 10, 15, 20. The sum of these proportional numbers 

 is 64, by which dividing 300, the quotient is 4 ac. 2r. 30 p., which being 

 multiplied by each of the numbers, 1, 2, 3, 5, &c. we obtain for the several 

 shares as annexed : 

 Ex. 3. It is required to divide 780 acres among A, B, and C, whose 



estates are 1,000, 3,000, and 4,000/. a year; the ground in their shares being worth 5, 8, and 10 



shillings the acre respectively. Here their claims are as 1, 3, 4; ^ ^. 492 



and the qualities of their land are as 5, 8, 10 ; therefore their quantities ^- -^ \ - 



must be as one-fifth, three-eighths, two-fifths, or by reduction, as 8, 



15, 16. Now the sum of these numbers is 39 ; by which dividing the 



780 acres, the quotient is 20; which being multiplied severally by the 



three numbers 8, 15, 16, the three products are 160, 300, 320, for 



the shares of A, B, C, respectively. 



3071. To cut off from a plan a given number of acres, 

 ^c. by a line drawn from any point in the side of it. 

 Rule. Let a {fig. 421.) be the given point in the ^ 

 plan, from which a line is to be drawn cutting off suppose J 

 5 ac. 2 r. 14 p. Draw a b cutting off the part ab c as near 

 as can be judged equal to the quantity proposed ; and let 

 the true quantity of a be, when calculated, be only 4 ac. 

 3^. 20 p. which is less than 5 ac. 2 r. 14 p. the true quan- 

 tity, by Oac. 2 r. 34 p. or 71,250 square links. Then measure al>, which suppose: 



